Equivalence of JST Algorithm and Kalman Filtering Algorithm for Time Scale Generation

Existing studies have established two different algorithms, the Kalman filtering algorithm and the Japan Standard Time (JST) algorithm, for generating reliable time scales. However, the relations between those two methods have not been clarified. In this paper, we mathematically clarify the equivalence of the averaged atomic time of JST-algo and Kalman filtering algorithm. In particular, we reveal the fact that the averaged atomic time of JST-algo does not depend on the measurement noise even though there is no filtering procedure in the algorithm. Furthermore, the prediction error of Kalman filtering algorithm is rigorously shown by using the prediction error regarding an observable state space. It is mathematically shown that when the covariance matrices of system noises are identical for all atomic clocks, then considering equal averaging weights for the clocks is a necessary and sufficient condition to ensure the equivalence between JST-algo and Kalman filtering algorithm. A numerical example comparing the runtime of JST-algo and Kalman filtering algorithm is provided to illustrate the efficacy of JST-algo.